Thread by @PausalZ

4: FORMAL CAUSAL INFERENCE (ATTIRE REQUESTED)
Math on twitter dot com? Should be fine /s
Shorter thread though

In Section 4.C we get a quirk of the deterministic results. Essentially within the deterministic system that nature created, the exposure pattern between t_0 and the end of the study has been ‘set’, no matter when outcomes occur. This is used to extend to competing risks

Here we get the written version of g-comp from Section 3. There is also the important point that g-comp can be applied to non-causal scenarios. However, when we do this there is less solid of interpretational foundations for the estimate

The assumptions are to link reality to the math formula. Without the assumptions about what happens in the world, the math is just a calculation exercise

However, evaluating equation 4.7 is difficult for anything besides a small number of follow-up times. Robins proposes using Monte Carlo instead

I did a quick thread on how you can think about interventions from a structured tree graph perspective with some animations

Robins concludes with an algorithm to reduce the complexity of the procedure. The procedure generates a coarser STG. While I don’t collapse the branches in my animation example, you can kinda see how non-time-varying exposures are a special case of a coarse STG